You can't exactly walk into a fine dining establishment off the street and expect to get hired as a sommelier, but you can achieve the title with much less training than for most other occupations. There are many courses available you can attend to become certified, many of them only lasting 6 months or so. You also won't rack up a ton of debt, as you can enroll in one of these programs for as little as $800 (although more often they'll be at least a couple grand).
After getting your Certified Sommeiler Certificate (redundant much?), you can go after your Advanced Sommelier Certificate, and eventually even your Master Sommelier Diploma, which basically tells people that you might as well have lived your entire life inside of a wine barrel for all you know about fine wines. You don't get to wear a special hat or anything, but people will be quite aware that you know your stuff.